Simplify the following expression: $q = \dfrac{-4y^2 + 12y + 280}{y + 7} $
First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-4$ , so we can rewrite the expression: $ q =\dfrac{-4(y^2 - 3y - 70)}{y + 7} $ Then we factor the remaining polynomial: $y^2 {-3}y {-70} $ ${7} {-10} = {-3}$ ${7} \times {-10} = {-70}$ $ (y + {7}) (y {-10}) $ This gives us a factored expression: $\dfrac{-4(y + {7}) (y {-10})}{y + 7}$ We can divide the numerator and denominator by $(y - 7)$ on condition that $y \neq -7$ Therefore $q = -4(y - 10); y \neq -7$